Time Series Foundation Model and Stochastic Functional Time Series Models for Dynamic Data-Driven Inference under Varying Operating States

Abstract. Dynamic Data-Driven Applications Systems (DDDAS) for complex engineering assets require time-series models that can assimilate streaming measurements, adapt to varying operating conditions, and support inference under uncertainty. This work compares two complementary modeling families: pretrained Time Series Foundation Models (TSFMs), represented by Tiny Time Mixers (TTM), and stochastic functional time-series models, represented by Functionally Pooled AutoRegressive (FP-AR) models. The comparison is conducted on active-sensing guided-wave structural health monitoring (SHM) and multicopter flighttest datasets. The models are evaluated through zero-shot and full-shot (head-probing) one-step-ahead prediction, in terms of prediction accuracy, representation quality, interpretability, and computational cost. The results clarify the practical tradeoffs between transferable foundationmodel representations and interpretable stochastic dynamical models for DDDAS-oriented inference.

Keywords: Dynamic Data-Driven Applications Systems · Time Series Foundation Models · Stochastic Functional Time Series Models · Structural Health Monitoring · Varying Operating Conditions · Drone Flight